2. (10 points) According to the life-cycle hypothesis individuals care about the PDV of their lifetime income in making current consumption decisions. As a result in our short run model, we have assumed consumption to be characterized as C def. However, now suppose that we also more accurately incorporated the role of interest rates and rewrote the consumption equation as, C=aY-6 (R-F) . (1) (a) Derive the new IS equation and show how the shape would be different from the original equation. (b) If the Federal reserve follows the simple monetary policy rule discussed in class, what would this imply for the slope of the aggregate demand curve?